The local existence of the solution follows immediately from a standard theory of delay differential equations,  [1]}. The non-negativity
follows from [2]}. To prove the global existence it is enough to use the step method and to observe that on the interval
\(\bigl [0,\tau _M\bigr ]\)  the system ((REF ), ()) becomes a system of non-autonomous ordinary differential equations. The
equation for \(p\)  becomes linear, it can be solved and then the equation for \(x\)  becomes linear with respect to \(x(t)\) .
